Semisupervised autoencoder for sentiment analysis

ABSTRACT

A method of modelling data, comprising: training an objective function of a linear classifier, based on a set of labeled data, to derive a set of classifier weights; defining a posterior probability distribution on the set of classifier weights of the linear classifier; approximating a marginalized loss function for an autoencoder as a Bregman divergence, based on the posterior probability distribution on the set of classifier weights learned from the linear classifier; and classifying unlabeled data using the autoencoder according to the marginalized loss function.

CROSS REFERENCE TO RELATED APPLICATIONS

The present application is a non-provisional of, and claims benefit of priority from, U.S. Provisional Patent Application No. 62/432,070, field Dec. 9, 2016, the entirety of which is expressly incorporated herein by reference.

GOVERNMENT LICENSE RIGHTS

This invention was made with government support under CCF-1017828 awarded by the National Science Foundation. The government has certain rights in the invention.

BACKGROUND OF THE INVENTION

In machine learning, documents are usually represented as Bag of Words (BoW), which nicely reduces a piece of text with arbitrary length to a fixed length vector. Despite its simplicity, BoW remains the dominant representation in many applications including text classification. There has also been a large body of work dedicated to learning useful representations for textual data (Turney and Pantel 2010; Blei, Ng, and Jordan 2003; Deerwester et al. 1990; Mikolov et al. 2013; Glorot, Bordes, and Bengio 2011). By exploiting the co-occurrence pattern of words, one can learn a low dimensional vector that forms a compact and meaningful representation for a document. The new representation is often found useful for subsequent tasks such as topic visualization and information retrieval. The application of one of the most popular representation learning methods, namely autoencoders (Bengio 2009), is applied to learn task-dependent representations for textual data. The present model naturally incorporates label information into its objective function, which allow the learned representation to be directly coupled with the task of interest.

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A specific class of task in text mining is addressed as an example of an application of the technology: Sentiment Analysis (SA). A special case of SA is addressed as a binary classification problem, where a given piece of text is either of positive or negative attitude. This problem is interesting largely due to the emergence of online social networks, where people consistently express their opinions about certain subjects. Also, it is easy to obtain a large amount of clean labeled data for SA by crawling reviews from websites such as IMDB or Amazon. Thus, SA is an ideal benchmark for evaluating text classification models (and features). However, the technology itself is not limited to this example.

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Autoencoders have attracted a lot of attention in recent years as a building block of Deep Learning (Bengio 2009). They act as the feature learning methods by reconstructing inputs with respect to a given loss function. In a neural network implementation of autoencoders, the hidden layer is taken as the learned feature. While it is often trivial to obtain good reconstructions with plain autoencoders, much effort has been devoted on regularizations in order to prevent them against overfitting (Bengio 2009; Vincent et al. 2008; Rifai et al. 2011b). However, little attention has been devoted to the loss function, which is important for modeling textual data. The problem with the commonly adopted loss functions (squared Euclidean distance and element-wise KL Divergence, for instance) is that they try to reconstruct all dimensions of input independently and indiscriminately. However, this is not the optimal approach when the interest is text classification. The reason is two-fold. First, it is well known that in natural language the distribution of word occurrences follows the power-law. This means that a few of the most frequent words will account for most of the probability mass of word occurrences. An immediate result is that the Autoencoder puts most of its effort on reconstructing the most frequent words well but (to a certain extent) ignores the less frequent ones. This may lead to a bad performance especially when the class distribution is not well captured by merely the frequent words. For sentiment analysis, this problem is especially severe because it is obvious that the truly useful features (words or phrases expressing a clear polarity) only occupy a small fraction of the whole vocabulary; and reconstructing irrelevant words such as ‘actor’ or ‘movie’ very well is not likely to help learn more useful representations to classify the sentiment of movie reviews. Second, explicitly reconstructing all the words in an input text is expensive, because the latent representation has to contain all aspects of the semantic space carried by the words, even if they are completely irrelevant. As the vocabulary size can easily reach the range of tens of thousands even for a moderate sized dataset, the hidden layer size has to be chosen very large to obtain a reasonable reconstruction, which causes a huge waste of model capacity and makes it difficult to scale to large problems.

In fact, the reasoning above applies to all the unsupervised learning methods in general, which is one of the most important problems to address in order to learn task-specific representations.

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In any labelled data, a bias may be incurred dependent on the labelling process. This bias may be a priori, that is, selectively creating the labels across the dataset with an intrinsic bias, or ex post facto, selecting data having a particular bias from a larger set of data, which itself may be biased or objective.

For example, subjective user feedback regarding a datum, compiled for that respective user, would generally lead to an a priori biased labelled dataset, representing the user's subjective responses, which may differ from responses of other members of the general population. Likewise, the bias need not be for a single individual, but may be representative of a family, company, group, community, demographic group, sex, age, race, national origin, sexual orientation, etc. In some cases, the user labels or characteristics are known in advance, and the labelled data classified according to the characteristics of the source. In this example, the classifications are predetermined, and the data may be segregated or labelled with the classification, and thereafter the data selective used based on its original classification or classification characteristics.

Alternately, the labelled data may be compiled without a predetermined classification of the source or bias represented, or predetermined grouping of the set of data pertinent to a particular class, and the available data about the user/source/bias stored as additional parameters of an unsegregated set of data. In this case, typically a larger pool of data may be available for analysis, and a subsequent process is employed to prepare or select the data for use.

In a multiparametric user/source/bias space, the data may be clustered using a statistical clustering algorithm, in order to automatically classify the user/source/bias, and perhaps the data content itself, either according to an automatically optimized classification/segmentation, or according to arbitrary or not predetermined classification at any time, including after collection of the labelled data. Further, according to a statistical process, data other than that within the selected class of user/source/bias may be exploited to provide improved statistical reliability, distinctive power, etc. For example, where the user/source/bias has an antithesis, the antithetical bias labelled data may be processed with the biased labelled data, weighted to improve decision-making between the two groups. Similarly, the weighting is not limited to opposites, and in a multiparametric classification space, each axis may have independent variation.

In some cases, the active learning process is not limited to a preprocessing of the data for later use in an autoencoder. Rather, the later process may be integrated with the user/source/bias classification, and this potentially rich classification data carrier through the analysis, for example as additional dimensions or degrees of freedom.

Data clustering is a process of grouping together data points having common characteristics. In automated processes, a cost function or distance function is defined, and data is classified is belonging to various clusters by making decisions about its relationship to the various defined clusters (or automatically defined clusters) in accordance with the cost function or distance function. Therefore, the clustering problem is an automated decision-making problem. The science of clustering is well established, and various different paradigms are available. After the cost or distance function is defined and formulated as clustering criteria, the clustering process becomes one of optimization according to an optimization process, which itself may be imperfect or provide different optimized results in dependence on the particular optimization employed. For large data sets, a complete evaluation of a single optimum state may be infeasible, and therefore the optimization process subject to error, bias, ambiguity, or other known artifacts.

In some cases, the distribution of data is continuous, and the cluster boundaries sensitive to subjective considerations or have particular sensitivity to the aspects and characteristics of the clustering technology employed. In contrast, in other cases, the inclusion of data within a particular cluster is relatively insensitive to the clustering methodology. Likewise, in some cases, the use of the clustering results focuses on the marginal data, that is, the quality of the clustering is a critical factor in the use of the system.

Clustering acts to effectively reduce the dimensionality of a data set by treating each cluster as a degree of freedom, with a distance from a centroid or other characteristic exemplar of the set. In a non-hybrid system, the distance is a scalar, while in systems that retain some flexibility at the cost of complexity, the distance itself may be a vector. Thus, a data set with 10,000 data points, potentially has 10,000 degrees of freedom, that is, each data point represents the centroid of its own cluster. However, if it is clustered into 100 groups of 100 data points, the degrees of freedom is reduced to 100, with the remaining differences expressed as a distance from the cluster definition. Cluster analysis groups data objects based on information in or about the data that describes the objects and their relationships. The goal is that the objects within a group be similar (or related) to one another and different from (or unrelated to) the objects in other groups. The greater the similarity (or homogeneity) within a group and the greater the difference between groups, the “better” or more distinct is the clustering.

It is noted that, in a text or semantic application, these degrees of freedom typically represent words, phrases, linkages, etc. In a labelled data application, the data set is supplemented with external and/or explicit labels, in addition to possible available information about the source or origin of the labels. While labelled data typically is static, when user, source, origin or other information about the labelling is updated after the labelling, that information may be propagated into the labelled data set.

In some cases, the dimensionality may be reduced to one, in which case all of the dimensional variety of the data set is reduced to a distance according to a distance function. This corresponds to a binary classification. This distance function may be useful, since it permits dimensionless comparison of the entire data set, and allows a user to modify the distance function to meet various constraints. Likewise, in certain types of clustering, the distance functions for each cluster may be defined independently, and then applied to the entire data set. In other types of clustering, the distance function is defined for the entire data set, and is not (or cannot readily be) tweaked for each cluster. Similarly, feasible clustering algorithms for large data sets preferably do not have interactive distance functions in which the distance function itself changes depending on the data. Many clustering processes are iterative, and as such produce a putative clustering of the data, and then seek to produce a better clustering, and when a better clustering is found, making that the putative clustering. However, in complex data sets, there are relationships between data points such that a cost or penalty (or reward) is incurred if data points are clustered in a certain way. Thus, while the clustering algorithm may split data points which have an affinity (or group together data points, which have a negative affinity, the optimization becomes more difficult.

Thus, for example, a semantic database may be represented as a set of documents with words or phrases. Words may be ambiguous, such as “apple”, representing a fruit, a computer company, a record company, and a musical artist. In order to effectively use the database, the multiple meanings or contexts need to be resolved. In order to resolve the context, an automated process might be used to exploit available information for separating the meanings, i.e., clustering documents according to their context. This automated process can be difficult as the data set grows, and in some cases the available information is insufficient for accurate automated clustering. On the other hand, a human can often determine a context by making an inference, which, though subject to error or bias, may represent a most useful result regardless.

In supervised classification, the mapping from a set of input data vectors to a finite set of discrete class labels is modeled in terms of some mathematical function including a vector of adjustable parameters. The values of these adjustable parameters are determined (optimized) by an inductive learning algorithm (also termed inducer), whose aim is to minimize an empirical risk function on a finite data set of input. When the inducer reaches convergence or terminates, an induced classifier is generated. In unsupervised classification, called clustering or exploratory data analysis, no labeled data are available. The goal of clustering is to separate a finite unlabeled data set into a finite and discrete set of “natural,” hidden data structures, rather than provide an accurate characterization of unobserved samples generated from the same probability distribution. In semi-supervised classification, a portion of the data are labeled, or sparse label feedback is used during the process.

Non-predictive clustering is a subjective process in nature, seeking to ensure that the similarity between objects within a cluster is larger than the similarity between objects belonging to different clusters. Cluster analysis divides data into groups (clusters) that are meaningful, useful, or both. If meaningful groups are the goal, then the clusters should capture the “natural” structure of the data. In some cases, however, cluster analysis is only a useful starting point for other purposes, such as data summarization. However, this often begs the question, especially in marginal cases; what is the natural structure of the data, and how do we know when the clustering deviates from “truth”? As discussed above, where labels may be biased, there may be different truths or a spectrum of different truths.

Many data analysis techniques, such as regression or principal component analysis (PCA), have a time or space complexity of O(m²) or higher (where m is the number of objects), and thus, are not practical for large data sets. However, instead of applying the algorithm to the entire data set, it can be applied to a reduced data set consisting only of cluster prototypes. Depending on the type of analysis, the number of prototypes, and the accuracy with which the prototypes represent the data, the results can be comparable to those that would have been obtained if all the data could have been used. The entire data set may then be assigned to the clusters based on a distance function.

Clustering algorithms partition data into a certain number of clusters (groups, subsets, or categories). Important considerations include feature selection or extraction (choosing distinguishing or important features, and only such features); Clustering algorithm design or selection (accuracy and precision with respect to the intended use of the classification result; feasibility and computational cost; etc.); and to the extent different from the clustering criterion, optimization algorithm design or selection.

Finding nearest neighbors can require computing the pairwise distance between all points. However, clusters and their cluster prototypes might be found more efficiently. Assuming that the clustering distance metric reasonably includes close points, and excludes far points, then the neighbor analysis may be limited to members of nearby clusters, thus reducing the complexity of the computation.

There are generally three types of clustering structures, known as partitional clustering, hierarchical clustering, and individual clusters. The most commonly discussed distinction among different types of clusterings is whether the set of clusters is nested or unnested, or in more traditional terminology, hierarchical or partitional. A partitional clustering is simply a division of the set of data objects into non-overlapping subsets (clusters) such that each data object is in exactly one subset. If the cluster shave sub-clusters, then we obtain a hierarchical clustering, which is a set of nested clusters that are organized as a tree. Each node (cluster) in the tree (except for the leaf nodes) is the union of its children (sub-clusters), and the root of the tree is the cluster containing all the objects. Often, but not always, the leaves of the tree are singleton clusters of individual data objects. A hierarchical clustering can be viewed as a sequence of partitional clusterings and a partitional clustering can be obtained by taking any member of that sequence; i.e., by cutting the hierarchical tree at a particular level.

There are many situations in which a point could reasonably be placed in more than one cluster, and these situations are better addressed by non-exclusive clustering. In the most general sense, an overlapping or non-exclusive clustering is used to reflect the fact that an object can simultaneously belong to more than one group (class). A non-exclusive clustering is also often used when, for example, an object is “between” two or more clusters and could reasonably be assigned to any of these clusters. In a fuzzy clustering, every object belongs to every cluster with a membership weight. In other words, clusters are treated as fuzzy sets. Similarly, probabilistic clustering techniques compute the probability with which each point belongs to each cluster.

In many cases, a fuzzy or probabilistic clustering is converted to an exclusive clustering by assigning each object to the cluster in which its membership weight or probability is highest. Thus, the inter-cluster and intra-cluster distance function is symmetric. However, it is also possible to apply a different function to uniquely assign objects to a particular cluster.

A well-separated cluster is a set of objects in which each object is closer (or more similar) to every other object in the cluster than to any object not in the cluster. Sometimes a threshold is used to specify that all the objects in a cluster must be sufficiently close (or similar) to one another. The distance between any two points in different groups is larger than the distance between any two points within a group. Well-separated clusters do not need to be spheric, but can have any shape.

If the data is represented as a graph, where the nodes are objects and the links represent connections among objects, then a cluster can be defined as a connected component; i.e., a group of objects that are significantly connected to one another, but that have less connected to objects outside the group. This implies that each object in a contiguity-based cluster is closer to some other object in the cluster than to any point in a different cluster.

A density-based cluster is a dense region of objects that is surrounded by a region of low density. A density-based definition of a cluster is often employed when the clusters are irregular or intertwined, and when noise and outliers are present. DBSCAN is a density-based clustering algorithm that produces a partitional clustering, in which the number of clusters is automatically determined by the algorithm. Points in low-density regions are classified as noise and omitted; thus, DBSCAN does not produce a complete clustering.

A prototype-based cluster is a set of objects in which each object is closer (more similar) to the prototype that defines the cluster than to the prototype of any other cluster. For data with continuous attributes, the prototype of a cluster is often a centroid, i.e., the average (mean) of all the points in the cluster. When a centroid is not meaningful, such as when the data has categorical attributes, the prototype is often a medoid, i.e., the most representative point of a cluster. For many types of data, the prototype can be regarded as the most central point. These clusters tend to be globular. K-means is a prototype-based, partitional clustering technique that attempts to find a user-specified number of clusters (K), which are represented by their centroids. Prototype-based clustering techniques create a one-level partitioning of the data objects. There are a number of such techniques, but two of the most prominent are K-means and K-medoid. K-means defines a prototype in terms of a centroid, which is usually the mean of a group of points, and is typically applied to objects in a continuous n-dimensional space. K-medoid defines a prototype in terms of a medoid, which is the most representative point for a group of points, and can be applied to a wide range of data since it requires only a proximity measure for a pair of objects. While a centroid almost never corresponds to an actual data point, a medoid, by its definition, must be an actual data point.

In the K-means clustering technique, we first choose K initial centroids, the number of clusters desired. Each point in the data set is then assigned to the closest centroid, and each collection of points assigned to a centroid is a cluster. The centroid of each cluster is then updated based on the points assigned to the cluster. Points may be iteratively assigned, and updated until convergence (no point changes clusters), or equivalently, until the centroids remain the same. For some combinations of proximity functions and types of centroids, K-means always converges to a solution; i.e., K-means reaches a state in which no points are shifting from one cluster to another, and hence, the centroids don't change. Because convergence tends to be asymptotic, the end condition may be set as a maximum change between iterations. Because of the possibility that the optimization results in a local minimum instead of a global minimum, errors may be maintained unless and until corrected. Therefore, a human assignment or reassignment of data points into classes, either as a constraint on the optimization, or as an initial condition, is possible.

To assign a point to the closest centroid, a proximity measure is required. Euclidean (L2) distance is often used for data points in Euclidean space, while cosine similarity may be more appropriate for documents. However, there may be several types of proximity measures that are appropriate for a given type of data. For example, Manhattan (L1) distance can be used for Euclidean data, while the Jaccard measure is often employed for documents. Usually, the similarity measures used for K-means are relatively simple since the algorithm repeatedly calculates the similarity of each point to each centroid, and thus complex distance functions incur computational complexity. The clustering may be computed as a statistical function, e.g., mean square error of the distance of each data point according to the distance function from the centroid. Note that the K-means may only find a local minimum, since the algorithm does not test each point for each possible centroid, and the starting presumptions may influence the outcome. The typical distance functions for documents include the Manhattan (L1) distance, Bregman divergence, Mahalanobis distance, squared Euclidean distance and cosine similarity.

An optimal clustering will be obtained as long as two initial centroids fall anywhere in a pair of clusters, since the centroids will redistribute themselves, one to each cluster. As the number of clusters increases, it is increasingly likely that at least one pair of clusters will have only one initial centroid, and because the pairs of clusters are further apart than clusters within a pair, the K-means algorithm will not redistribute the centroids between pairs of clusters, leading to a suboptimal local minimum. One effective approach is to take a sample of points and cluster them using a hierarchical clustering technique. K clusters are extracted from the hierarchical clustering, and the centroids of those clusters are used as the initial centroids. This approach often works well, but is practical only if the sample is relatively small, e.g., a few hundred to a few thousand (hierarchical clustering is expensive), and K is relatively small compared to the sample size. Other selection schemes are also available.

The space requirements for K-means are modest because only the data points and centroids are stored. Specifically, the storage required is O(m+K)^(n), where m is the number of points and n is the number of attributes. The time requirements for K-means are also modest—basically linear in the number of data points. In particular, the time required is O(I×K×m×n), where I is the number of iterations required for convergence. I is often small and can usually be safely bounded, as most changes typically occur in the first few iterations. Therefore, K-means is linear in m, the number of points, and is efficient as well as simple provided that K, the number of clusters, is significantly less than m.

Outliers can unduly influence the clusters, especially when a squared error criterion is used. However, in some clustering applications, the outliers should not be eliminated or discounted, as their appropriate inclusion may lead to important insights. In some cases, such as financial analysis, apparent outliers, e.g., unusually profitable investments, can be the most interesting points.

Hierarchical clustering techniques are a second important category of clustering methods. There are two basic approaches for generating a hierarchical clustering: Agglomerative and divisive. Agglomerative clustering merges close clusters in an initially high dimensionality space, while divisive splits large clusters. Agglomerative clustering relies upon a cluster distance, as opposed to an object distance. For example, the distance between centroids or medioids of the clusters, the closest points in two clusters, the further points in two clusters, or some average distance metric. Ward's method measures the proximity between two clusters in terms of the increase in the sum of the squares of the errors that results from merging the two clusters.

Agglomerative Hierarchical Clustering refers to clustering techniques that produce a hierarchical clustering by starting with each point as a singleton cluster and then repeatedly merging the two closest clusters until a single, all-encompassing cluster remains. Agglomerative hierarchical clustering cannot be viewed as globally optimizing an objective function. Instead, agglomerative hierarchical clustering techniques use various criteria to decide locally, at each step, which clusters should be merged (or split for divisive approaches). This approach yields clustering algorithms that avoid the difficulty of attempting to solve a hard combinatorial optimization problem. Furthermore, such approaches do not have problems with local minima or difficulties in choosing initial points. Of course, the time complexity of O(m² log m) and the space complexity of O(m²) are prohibitive in many cases. Agglomerative hierarchical clustering algorithms tend to make good local decisions about combining two clusters since they can use information about the pair-wise similarity of all points. However, once a decision is made to merge two clusters, it cannot be undone at a later time. This approach prevents a local optimization criterion from becoming a global optimization criterion.

In supervised classification, the evaluation of the resulting classification model is an integral part of the process of developing a classification model. Being able to distinguish whether there is non-random structure in the data is an important aspect of cluster validation.

Each of the following is expressly incorporated herein by reference in its entirety, for example, for its disclosure of clustering technology, applications of that technology, and implementations: U.S. Pat. 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When humans having preferences or profiles are involved as the source of data labels, various technologies have developed to facilitate the process. For example, a user may be classified with other users having similar tastes or classification criteria using collaborative filters.

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Cohen et al, Cohn, David A., Ghahramani, Zoubin, and Jordan, Michael I., “Active Learning with Statistical Models”, Center for Biological and Computational Learning, Dept. of Brain and Cognitive Sciences, MIT, Cambridge, Mass., (1996) www.cs.cmu.edu/afs/cs/project/jair/pub/volume4/cohn96a-html/statmodels.html, provides a review of active learning. A goal of machine learning is to create systems that can improve their performance at some task as they acquire experience or data. In many natural learning tasks, this experience or data is gained interactively, by taking actions, making queries, or doing experiments. Most machine learning research, however, treats the learner as a passive recipient of data to be processed. This “passive” approach ignores the fact that, in many situations, the learner's most powerful tool is its ability to act, to gather data, and to influence the world it is trying to understand. Active learning is the study of how to use this ability effectively. Formally, active learning studies the closed-loop phenomenon of a learner selecting actions or making queries that influence what data are added to its training set. Examples include selecting joint angles or torques to learn the kinematics or dynamics of a robot arm, selecting locations for sensor measurements to identify and locate buried hazardous wastes, or querying a human expert to classify an unknown word in a natural language understanding problem.

When actions/queries are selected properly, the data requirements for some problems decrease drastically, and some NP-complete learning problems become polynomial in computation time [Angluin 1988, Baum & Lang 1991]. In practice, active learning offers its greatest rewards in situations where data are expensive or difficult to obtain, or when the environment is complex or dangerous. In industrial settings each training point may take days to gather and cost thousands of dollars; a method for optimally selecting these points could offer enormous savings in time and money. There are a number of different goals which one may wish to achieve using active learning. One is optimization, where the learner performs experiments to find a set of inputs that maximize some response variable. An example of the optimization problem would be finding the operating parameters that maximize the output of a steel mill or candy factory. The favored technique for this kind of optimization is usually a form of response surface methodology [Box & Draper 1987], which performs experiments that guide hill-climbing through the input space.

A related problem exists in the field of adaptive control, where one must learn a control policy by taking actions. In control problems, one faces the complication that the value of a specific action may not be known until many time steps after it is taken. Also, in control (as in optimization), one is usually concerned with the performing well during the learning task and must trade of exploitation of the current policy for exploration which may improve it. The subfield of dual control [Fe'ldbaum 1965] is specifically concerned with finding an optimal balance of exploration and control while learning. Mixtures of Gaussians and locally weighted regression are two statistical models that offer elegant representations and efficient learning algorithms.

Therefore, it is understood that the sentiment analysis problem in particular, or the classification problem in general, may employ objectively or subjectively labelled data, and in the latter case, a subjective analysis performed. The subjective bias may be as an initial filtering or selection, or may be statistical as a predicate or integrated process.

SUMMARY OF THE INVENTION

The usage of autoencoders is provided for modeling textual data. Traditional autoencoders suffer from at least two aspects: scalability with the high dimensionality of vocabulary size and dealing with task-irrelevant words. This problem is addressed by introducing supervision via the loss function of autoencoders. In particular, a linear classifier is first trained on the labeled data, then a loss for the autoencoder defined with the weights learned from the linear classifier. To reduce the bias brought by one single classifier, a posterior probability distribution is defined on the weights of the classifier, and the marginalized loss of the autoencoder derived with a Laplace approximation. The choice of loss function can be rationalized from the perspective of Bregman Divergence, which justifies the soundness of the model. The effectiveness of the model was evaluated on six sentiment analysis datasets, and was shown to significantly outperform all the competing methods with respect to classification accuracy. The model is able to take advantage of unlabeled datasets and get improved performance. The model successfully learns highly discriminative feature maps, which explains its superior performance.

According to the present technology, the semisupervised approach is adopted, where label information is introduced to guide the feature learning procedure. In particular, a novel loss function is provided for training autoencoders that are directly coupled with the classification task. A linear classifier is first trained on BoW, then a Bregman Divergence [Banerjee et al. 2004] is derived as the loss function of a subsequent autoencoder. The new loss function gives the autoencoder the information about directions along which the reconstruction should be accurate, and where larger reconstruction errors are tolerated. Informally, this can be considered as a weighting of words based on their correlations with the class label: predictive words should be given large weights in the reconstruction even they are not frequent words, and vice versa. Furthermore, to reduce the bias introduced by the linear classifier, a Bayesian view is adopted by defining a posterior distribution on the weights of the classifier. The posterior is then approximated with a Laplace approximation and the marginalized loss function derived for the autoencoder. The present model successfully learns features that are highly discriminative with respect to class labels, and also outperform all the competing methods evaluated by classification accuracy. Moreover, the derived loss can also be applied to unlabeled data, which allows the model to learn further better representations.

It is therefore an object to provide a method of modelling data, comprising: training an objective function of a linear classifier, based on a set of labeled data, to derive a set of classifier weights; defining a posterior probability distribution on the set of classifier weights of the linear classifier; approximating a marginalized loss function for an autoencoder as a Bregman divergence, based on the posterior probability distribution on the set of classifier weights learned from the linear classifier; and classifying unlabeled data using a compact classifier according to the marginalized loss function.

It is also an object to provide a system for modelling data, comprising: an input port, configured to receive a set of labelled data; a linear classifier; an autoencoder; a compact classifier, and an output port, configured to communicate a classification of at least one unlabeled datum, wherein: an objective function of a linear classifier is automatically trained, based on the set of labeled data, to derive a set of classifier weights; a marginalized loss function for the compact classifier approximated as a Bregman divergence, based on a posterior probability distribution on the set of classifier weights learned from the linear classifier; and the at least one unlabeled datum classified using a compact classifier according to the marginalized loss function.

It is another object to provide a computer readable medium containing non-transitory instructions for controlling at least one programmable automated processor to perform a method of modelling data, comprising: training an objective function of a linear classifier, based on a set of labeled data, to derive a set of classifier weights; defining a posterior probability distribution on the set of classifier weights of the linear classifier; approximating a marginalized loss function for an autoencoder as a Bregman divergence, based on the posterior probability distribution on the set of classifier weights learned from the linear classifier; and classifying unlabeled data using a compact classifier according to the marginalized loss function. The data may comprise semantic data, textual data, and may consist essentially of text documents.

The autoencoder may comprise a neural network, wherein said training comprises training the neural network. The autoencoder may be a denoising autoencoder. The denoising autoencoder may be denoised stochastically. The denoising autoencoder may comprise a neural network trained according to stochastic gradient descent training using randomly selected data samples, wherein a gradient is calculated using back propagation of errors. The training may comprise training the objective function of the linear classifier with a bag of words, wherein the linear classifier comprises a support vector machine classifier with squared hinge loss and l₂ regularization. The training may comprise training the objective function of the linear classifier with a bag of words, wherein the linear classifier comprises a Logistic Regression classifier.

The Bregman divergence may be determined assuming that all data samples induce a loss. The posterior probability distribution on the set of classifier weights may be estimated using with a Laplace approximation. The Laplace approximation may stochastically estimate the set of classifier weights using a covariance matrix constrained to be diagonal. The posterior probability distribution on the set of classifier weights may be estimated using with a Markov chain Monte Carlo method.

The labelled data may be sentiment data, user preferences, social network data/documents, newsfeed, email, or other types of documents or semantic information, and in some cases multimodal data or non-semantic data, though preferably the data has semantic content amenable to analysis. Because the method is statistical and not cognitive, the basis for the labelling may be arbitrary, and sentiment analysis is but one example. The labelling may be objective, in which case the system provides an objective classification or output. On the other hand, the labelling may be subjective or biased, and the particular subject group or bias may provide an additional input to the system where the set of labeled data is polydiverse. When subjective or biased data is provided, the system may be trained initially with a filter applied to the received data, so that the first classifier is trained only with labelled data with the correct bias. A plurality of first classifiers, autoencoders, and second classifiers may therefore be provided for the range of labelled data biases.

On the other hand, the data which defines or distinguishes the bias or potential bias may be carrier through to the first classifier, without filtering or blocking data which does not meet a specific subjective classification requirement. The first classifier may then operate with the subject user/source/bias information as additional dimensions or degrees of freedom, and produce an analysis that maintains the range of bias. The learning transfer process may then resolve the bias, and thus transfer the learning to the autoencoder in a manner to eliminate these additional degrees of freedom, or pass through the range of subjective bias to the autoencoder and second classifier (compact classifier). In the latter case, the system may then learn the desired bias of the system through an explicit, implicit, feedback, or adaptive algorithm, to provide a suitable output.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a process flow of an embodiment of the invention.

FIG. 2 shows a preferred embodiment of a process flow of the invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Model

Denoising Autoencoders

Autoencoders learn functions that can reconstruct the inputs. They are typically implemented as a neural network with one hidden layer, and one can extract the activation of the hidden layer as the new representation. Mathematically, a collection of data points X={xi}, xi∈Rd, i∈[1, m] is provided, and the objective function of an autoencoder is thus:

$\begin{matrix} {{\min\;{\sum\limits_{i}D_{({{\overset{\sim}{x}}_{i},x_{i}})}}}{{{s.t.\mspace{14mu} h_{i}} = {g\left( {{Wx}_{i} + b} \right)}},{{\overset{\sim}{x}}_{i} = {f\left( {{W^{\prime}h_{i}} + b^{\prime}} \right)}}}} & (1) \end{matrix}$

where W∈R^(k×d), b∈R^(k), W′∈R^(d×k) bl∈Rd are the parameters to be learned; D is a loss function, such as the squared Euclidean Distance ∥x−x∥₂ ², g and ƒ are predefined nonlinear functions, which is set as g(x)=max(0,x), ƒ(x)=(1+exp(−x))⁻¹; h_(i) is the learned representation; {tilde over (x)}_(i) is the reconstruction. A common approach is to use tied weights by setting W=Wl; this usually works better as it speeds up learning and prevents overfitting at the same time. For this reason, tied weights are employed herein.

Autoencoders transform an unsupervised learning problem to a supervised one by the self-reconstruction criteria. This enables one to use all the tools developed for supervised learning such as back propagation to efficiently train the autoencoders. Moreover, thanks to the nonlinear functions ƒ and g, autoencoders are able to learn non-linear and possibly overcomplete representations, which give the model much more expressive power than their linear counter parts such as PCA (LSA) [Deerwester et al. 1990].

One of the most popular variants of autoencoders is adopted, namely the Denoising Autoencoder. A Denoising Autoencoder works by reconstructing the input from a noised version of itself. The intuition is that a robust model should be able to reconstruct the input well even in the presence of noises, due to the high correlation among features. For example, imagine deleting or adding a few words from/to a document, the semantics should still remain unchanged, thus the autoencoder should learn a consistent representation from all the noisy inputs. In the high level, Denoising Autoencoders are equivalent to ordinary autoencoders trained with dropout [Srivastava et al. 2014], which has been shown as an effective regularizer for (deep) neural networks. Formally, let q(x|x) be a predefined noising distribution, and x be a noised sample of x:x˜q(x|x). The objective function takes the form of sum of expectations over all the noisy samples:

$\begin{matrix} {{\min\;{\sum\limits_{i}{E_{q{({{\overset{\_}{x}}_{i}❘x_{i}})}}D_{({{\overset{\sim}{x}}_{i},x_{i}})}}}}{{{s.t.\mspace{14mu} h_{i}} = {g\left( {{W\;{\overset{\_}{x}}_{i}} + b} \right)}},{{\overset{\sim}{x}}_{i} = {f\left( {{W^{\prime}h_{i}} + b^{\prime}} \right)}}}} & (2) \end{matrix}$

The notation is slightly overloaded, to let {tilde over (x)}_(i) denote the reconstruction calculated from the noised input x _(i). While the marginal objective function requires infinite many noised samples per data point, in practice it is sufficient to simulate it stochastically. That is, for each example seen in the stochastic gradient descent training, a x _(i) is randomly sampled from q(x|x) and calculate the gradient with ordinary back propagation.

Loss Function as Bregman Divergence

The proper choice of the loss function D in (2) is a specific form of Bregman Divergence. Bregman Divergence [Banerjee et al. 2004] generalizes the notion of distance in a d dimensional space. To be concrete, given two data points {tilde over (x)}, x∈R^(d) and a convex function ƒ(x) defined on R^(d), the Bregman Divergence of {tilde over (x)} from x with respect to ƒ is: D _(ƒ)({tilde over (x)},x)=ƒ({tilde over (x)})−ƒ(x)+∇ƒ(x)^(T)({tilde over (x)}−x))  (3)

Namely, Bregman Divergence measures the distance between two points {tilde over (x)},x as the deviation between the function value of ƒ and the linear approximation of ƒ around x at {tilde over (x)}.

Two of the most commonly used loss functions for autoencoders are the squared Euclidean distance and elementwise KL divergence. It is not difficult to verify that they both fall into this family by choosing ƒ as the squared l₂ norm and the sum of element-wise entropy respectively. What the two loss functions have in common is that they make no distinction among dimensions of the input. In other words, each dimension of the input is pushed to be reconstructed equally well. While autoencoders trained in this way have been shown to work very well on image data, learning much more interesting and useful features than the original pixel intensity features, they are less appropriate for modeling textual data. The reason is two folds. First, textual data are extremely sparse and high dimensional, where the dimensionality is equal to the vocabulary size. To maintain all the information of the input in the hidden layer, a very large layer size must be adopted, which makes the training cost extremely large. Second, ordinary autoencoders are not able to deal with the power law of word distributions, where a few of the most frequent words account for most of the word occurrences. As a result, frequent words naturally gain favor to being reconstructed accurately, and rare words tend to be reconstructed with less precision. This problem is also analogous to the imbalanced classification setting. This is especially problematic when frequent words carry little information about the task of interest, which is not uncommon. Examples include stop words (the, a, this, from) and topic related terms (movie, watch, actress) in a movie review sentiment analysis task.

Semisupervised Autoencoder with Bregman Divergence

To address the problems mentioned above, introduction of supervision to the training of autoencoders is proposed. To achieve this, a linear classifier is first trained on Bag of Words, and then the weight of the learned classifier used to define a new loss function for the autoencoder. Now let us first describe our choice of loss function, and then elaborate the motivation later: D({tilde over (x)},x)=(θ^(T)({tilde over (x)}−x))²  (4) where θ∈R^(d) are the weights of the linear classifier, with the bias omitted for simplicity. Note that Equation (4) is a valid distance, as it is non-negative and reaches zeros if and only if {tilde over (x)}=x. Moreover, the reconstruction error is only measured after projecting on θ; this guides the reconstruction to be accurate only along directions where the linear classifier is sensitive to. Note also that Equation (4) on the one hand uses label information (θ has been trained with labeled data), on the other hand no explicit labels are directly referred to (only requires x_(i)). Thus one is able to train an autoencoder on both labeled and unlabeled data with the loss function in Equation (4). This subtlety distinguishes our method from pure supervised or unsupervised learning, and allows us to enjoy the benefit from both worlds.

As a design choice, SVM is considered with squared hinge loss (SVM2) and l₂ regularization as the linear classifier, but other classifiers such as Logistic Regression can be used and analyzed similarly. See, en.wikipedia.org/wiki/Support_vector_machine; www.robots.ox.ac.uk/˜az/lectures/ml/lect2.pdf; www.cs.columbia.edu/˜kathy/cs4701/documents/jason_svm_tutorial.pdf; en.wikipedia.org/wiki/Hinge_loss; www.csie.ntu.edu.tw/˜cjlin/papers/l2mcsvm/l2mcsvm.pdf; www.vlfeat.org/api/svm-advanced.html; www.jmlr.org/papers/volume4/steinwart03a/steinwart03a.pdf; arxiv.org/pdf/1306.0239.pdf. Denote {x_(i)}, x_(i)∈R^(d) as the collection of samples, and {y_(i)}, y_(i)∈[1,−1] as the class labels; with the objective function SVM2 is:

$\begin{matrix} {{L(\theta)} = {{\sum\limits_{i}\left( {\max\left( {0,{1 - {y_{i}\theta^{T}x_{i}}}} \right)} \right)^{2}} + {\lambda{\theta }^{2}}}} & (5) \end{matrix}$ Here θ∈R^(d) is the weight, λ is the weight decay parameter.

Equation (5) is continuous and differentiable everywhere with respect to θ, so the model can be easily trained with stochastic gradient descent.

The next (and perhaps critical) step of the present approach is to transfer label information from the linear classifier to the autoencoder. See, Weiss, K., Khoshgoftaar, T. M. & Wang, D. J Big Data (2016) 3: 9. doi:10.1186/s40537-016-0043-6, which provide a survey of transfer learning.

With this in mind, the loss induced by each sample as a function of the input is examined, while with θ fixed: ƒ(x _(i))=(max(0,1−y _(i)θ^(T) x _(i)))²  (6)

Note that ƒ(x_(i)) is defined on the input space R^(d), which should be contrasted with L(θ) in Equation (5) which is a function of θ. ƒ(x_(i)) is of interest, because considering moving each input x_(i) to {tilde over (x)}_(i), ƒ(x_(i)) indicates the direction along which the loss is sensitive to. {tilde over (x)} can be thought of as the reconstruction of x_(i) obtained from an autoencoder, so a good {tilde over (x)} should be in a way such that the deviation of {tilde over (x)} from x_(i) is small evaluated by ƒ(x_(i)). In other words, {tilde over (x)} is sought to still be correctly classified by the pretrained linear classifier. Therefore, ƒ(x_(i)) should be a much better function to evaluate the deviation of two samples. A Bregman Divergence is derived from ƒ(x_(i)) and used as the loss function of the subsequent autoencoder training, so that the autoencoder is guided to give reconstruction errors that do not confuse the classifier. Note that ƒ(x_(i)) is a quadratic function of x_(i) whenever ƒ(x_(i))>0, the Hessian matrix is derived in order to achieve the Bregman Divergence.

The Hessian follows as:

$\begin{matrix} {{H\left( x_{i} \right)} = \left\{ {\begin{matrix} {{\theta\;\theta^{T}},} & {{{{if}\mspace{14mu} 1} - {y_{i}\theta^{T}x_{i}}} > 0} \\ {0,} & {otherwise} \end{matrix}.} \right.} & (7) \end{matrix}$

For a quadratic function with Hessian matrix H, the Bregman Divergence is simply ({tilde over (x)}−x)^(T)H({tilde over (x)}−x); leading to:

$\begin{matrix} {{D\left( {\overset{\sim}{x},x_{i}} \right)} = \left\{ {\begin{matrix} {\left( {\theta^{T}\left( {{\overset{\sim}{x}}_{i} - x_{i}} \right)} \right)^{2},} & {{{{if}\mspace{14mu} 1} - {y_{i}\theta^{T}x_{i}}} > 0} \\ {0,} & {otherwise} \end{matrix}.} \right.} & (8) \end{matrix}$

In words, Equation (8) says that the reconstruction loss for difficult examples (those that satisfy 1−y_(i)θ^(T)x_(i)>0) is measured with Equation (4); and there is no reconstruction loss at all for easy examples. This discrimination is undesirable, because in this case the Autoencoder would completely ignore easy examples, and there is no way to guarantee that the {tilde over (x)}_(i) can be correctly classified. Actually, this split is just an artifact of the hinge loss and the asymmetrical property of Bregman Divergence. Hence, a simple correction is performed by ignoring the condition in Equation (8), which basically pretends that all the examples induce a loss. This directly yields the loss function as in Equation (4).

The Bayesian Marginalization

In principle, one may directly apply Equation (4) as the loss function in place of the squared Euclidean distance and train an autoencoder. However, doing so might introduce a bias brought by one single classifier. As a remedy, the Bayesian approach is resorted to, which defines a probability distribution over θ.

Although SVM2 is not a probabilistic classifier like Logistic Regression, the idea of Energy Based Model (Bengio 2009) can be borrowed, and L(θ) used as the negative log likelihood of the following distribution:

$\begin{matrix} {{p(\theta)} = \frac{\exp\left( {{- \beta}\;{L(\theta)}} \right)}{\int{{\exp\left( {{- \beta}\;{L(\theta)}} \right)}d\;\theta}}} & (9) \end{matrix}$ where β>0 is the temperature parameter which controls the shape of the distribution p. Note that the larger β is, the sharper p will be. In the extreme case, p(θ) is reduced to a uniform distribution as β approaches 0, and collapses into a single δ function as β goes to positive infinity.

Given p(θ), Equation (4) is rewritten as an expectation over θ: D({tilde over (x)},x)=E _(θ˜p(θ))(θ^(T)({tilde over (x)}−x))²=∫(θ^(T)({tilde over (x)}−x))² p(θ)dθ  (10)

Obviously there is now no closed form expression for D({tilde over (x)}, x). To solve it one could use sampling methods such as MCMC, which provides unbiased estimates of the expectation but could be slow in practice. See, en.wikipedia.org/wiki/Markov_chain_Monte_Carlo; www.mcmchandbook.net/HandbookChapter1.pdf; twiecki.github.io/blog/2015/11/10/mcmc-sampling/; www.cs.cornell.edu/selman/cs475/lectures/intro-mcmc-lukas.pdf; www.cs.princeton.edu/courses/archive/spr06/cos598C/papers/AndrieuFreitasDoucetJordan2003.pdf.

Instead, the Laplace approximation is used, which approximates p(θ) by a Gaussian distribution {tilde over (p)}(θ), N ({circumflex over (θ)}, Σ).

To see this, by simply replacing p(θ) with {tilde over (p)}(θ) in Equation (11):

$\begin{matrix} \begin{matrix} {{D\left( {\overset{\sim}{x},x} \right)} = {E_{\theta \sim {\overset{\sim}{p}{(\theta)}}}\left( {\theta^{T}\left( {\overset{\sim}{x} - x} \right)} \right)}^{2}} \\ {= {\left( {\overset{\sim}{x} - x} \right)^{T}{E_{\theta \sim {\overset{\sim}{p}(\theta}}\left( {\theta\;\theta^{T}} \right)}\left( {\overset{\sim}{x} - x} \right)}} \\ {= {\left( {\overset{\sim}{x} - x} \right)^{T}\left( {{\theta\;\theta^{T}} + \Sigma} \right)\left( {\overset{\sim}{x} - x} \right)}} \\ {= {\left( {{\hat{\theta}}^{T}\left( {\overset{\sim}{x} - x} \right)} \right)^{2} + {\left( {\Sigma^{1/2}\left( {\overset{\sim}{x} - x} \right)} \right)^{T}\left( {\Sigma^{1/2}\left( {\overset{\sim}{x} - x} \right)} \right)}}} \end{matrix} & (11) \end{matrix}$ where D now involves two parts, corresponding to the mean and variance term of the Gaussian distribution respectively. Now let us derive {tilde over (p)}(θ) for p(θ). In Laplace approximation, {circumflex over (θ)} is chosen as the mode of p(θ), which is exactly the solution to the SVM2 optimization problem. For Σ:

$\begin{matrix} {\left. {\Sigma = {{diag}\left( \frac{\partial^{2}{L(\theta)}}{\partial\theta^{2}} \right)}} \right)^{- 1}{\frac{1}{\beta}\left( {{diag}\left( {\sum\limits_{i}{{I\left( {{1 - {y_{i}\theta^{T}x_{i}}} > 0} \right)}x_{i}^{2}}} \right)} \right)^{- 1}}} & (12) \end{matrix}$

Here diag is overridden, letting it denote a diagonal matrix induced either by a square matrix or a vector; I is the indicator function; (⋅)⁻¹ denotes matrix inverse. Interestingly, the second term in Equation (11) is now equivalent to the squared Euclidean distance after performing element-wise normalizing the input using all difficult examples. The effect of this normalization is that the reconstruction errors of frequent words are down weighted; on the other hand, discriminative words are given higher weights as they would occur less frequently in difficult examples. Note that it is important to use a relatively large β in order to avoid the variance term dominating the mean term. In other words, p(θ) is assured to be reasonably peaked around {circumflex over (θ)} to effectively take advantage of label information.

TABLE 1 Statistics of the datasets. IMDB books DVD music electronics kitchenware # train 25,000 10,000 10,000 18,000 6,000 6,000 # test 25,000 3,105 2,960 2,661 2,862 1,691 # unlabeled 50,000 N/A N/A N/A N/A N/A # features 8,876 9,849 10,537 13,099 5,091 3,907 % positive 50 49.81 49.85 50.16 49.78 50.08 ai.stanford.edu/amaas/data/sentiment/ www.cs.jhu.edu/mdredze/datasets/sentiment/

Experiments

Datasets

The model is evaluated on six Sentiment Analysis benchmarks. The first one is the IMDB dataset (ai.stanford.edu/amaas/data/sentiment/) (Maas et al. 2011), which consists of movie reviews collected from IMDB. The IMDB dataset is one of the largest sentiment analysis dataset that is publicly available; it also comes with an unlabeled set which allows us to evaluate semisupervised learning methods. The rest five datasets are all collected from Amazon (www.cs.jhu.edu/mdredze/datasets/sentiment/) (Blitzer, Dredze, and Pereira 2007), which corresponds to the reviews of five different products: books, DVDs, music, electronics, kitchenware. All the six datasets are already tokenized as either uni-gram or bi-gram features. For computational reasons, only the words that occur in at least 30 training examples are selected. The statistics of datasets are summarized in Table 1.

Methods

-   -   Bag of Words (BoW). Instead of using the raw word counts         directly, a simple step of data normalization is performed:

$\begin{matrix} {x_{i,j} = \frac{\log\left( {1 + c_{i,j}} \right)}{\max_{j}{\log\left( {1 + c_{i,j}} \right)}}} & (13) \end{matrix}$ where c_(i,j) denotes the number of occurrences of the j^(th) word in the i^(th) document, x_(i,j) denotes the normalized count. This normalization was chosen because it preserves the sparsity of the Bag of Words features; also each feature element is normalized to the range [0, 1]. Note that the very same normalized Bag of Words features are fed into the autoencoders.

-   -   Den         ising Autoencoder (DAE) [Vincent et al. 2008]. This refers to         the regular Denoising Autoencoder defined in Equation (1) with         squared Euclidean distance loss: D({tilde over (x)},x)=∥{tilde         over (x)}−x∥₂ ². This is also used in [Glorot, Bordes, and         Bengio 2011] on the Amazon datasets for domain adaptation. ReLu         max(0, x) is used as the activation function, and Sigmoid as the         decoding function.     -   Denoising Autoencoder with Finetuning (DAE+) [Vincent et al.         2008]. This denotes the common approach to continue training an         DAE on labeled data by replacing the decoding part of DAE with a         Softmax layer.     -   Feedforward Neural Network (NN). This is the standard fully         connected neural network with one hidden layer and random         initialization. The same activation function is used as that in         Autoencoders, i.e., Rectified Linear Activation Unit (ReLU).     -   Logistic Regression with Dropout (LrDrop) (Wager, Wang, and         Liang 2013). This is a model where logistic regression is         regularized with the marginalized dropout noise. LrDrop differs         from the present approach as it uses feature noising as an         explicit regularization. Another difference is that the present         technology is able to learn nonlinear representations, not         merely a classifier, and thus is potentially able to model more         complicated patterns in data.     -   Semisupervised Bregman Divergence Autoencoder (SBDAE). This         corresponds to the present model with Denoising Autoencoder as         the feature learner. The training process is roughly equivalent         to training on BoW followed by the training of DAE, except that         the loss function of DAE is replaced with the loss function         defined in Equation (11). β is cross-validated from the set         {10⁴, 10⁵, 10⁶, 10⁷, 10⁸} (note that larger β corresponds to         weaker Bayesian regularization).     -   Semisupervised Bregman Divergence Autoencoder with Finetuning         (SBDAE+). Note that except for BoW and LrDrop, all the other         methods require a predefined dimensionality of representation.         Fixed sizes were used on all the datasets. For SBDAE and NN, a         small hidden size is sufficient, so 200 was used. For DAE, it is         observed that it benefits from very large hidden sizes; however,         due to computational constraints, 2000 were taken. For BoW, DAE,         SBDAE, SVM2 is used as the classifier. All the models are         trained with mini-batch Stochastic Gradient Descent with         momentum of 0.9.

As shown in FIG. 1, a set of labeled data is received 101. A first classifier is trained on the labeled data 102, and a set of classifier weights derived 103. The weights are then transferred for use by an autoencoder, by defining a stochastic posterior probability distribution on the set of weights 104, with an approximated marginalized loss function 105. A second classifier is trained based on the representation of the autoencoder 106. In use, a system employing the autoencoder receives unlabeled data 107, and generates classifications of the received data 108. After the learning transfer, the linear classifier is not required for use by the system, though for adaptive learning, the training and learning transfer may be periodic or continuous.

FIG. 2 shows a preferred embodiment of the method. The labelled set of data is received 201, and used to train a classifier, which in this case is an artificial neural network trained on a “bag of words” representation of the labeled data, using SVM2 with squared hinge loss and l₂ regularization as the linear classifier 202. The trained set of weights is then exported in a learning transfer process, to a denoising autoencoder 203. Using a statistical method, a posterior probability distribution on the set of weights is defined 204, for example using a Laplace approximation, to define the approximate marginalized loss function of the denoising autoencoder 205. A representation of the denoising autoencoder is then used to train a classifier 206. In use, a system employing the classifier receives unlabeled data 207, and generates classifications of the received data 208.

Results

The results are summarized as classification error rate in Table 2. First of all, the present technology consistently beats BoW with a margin, and it achieves the best results on four (larger) datasets out of six. On the other hand, DAE, DAE+ and NN all fail to outperform BoW, although they share the same architecture as nonlinear classifiers. This suggests that SBDAE is able to learn a much better nonlinear feature transformation function by training with a more informed objective (than that of DAE). Moreover, note also that finetuning on labeled set (DAE+) significantly improves the performance of DAE, which is ultimately on a par with training a neural net with random initialization (NN). However, finetuning offers little help to SBDAE, as it is already implicitly guided by labels during the training.

LrDrop is the second best method tested. Thanks to the usage of dropout regularization, it consistently outperforms BoW, and achieves the best results on two (smaller) datasets. Compared with LrDrop, it appears that the present technology works better on large datasets (≈10K words, more than 10K training examples) than smaller ones. This indicates that in high dimensional spaces with sufficient samples, SBDAE benefits from learning a nonlinear feature transformation that disentangles the underlying factors of variation, while LrDrop is incapable of doing so due to its nature as a linear classifier.

As the training of the autoencoder part of SBDAE does not require the availability of labels, incorporating unlabeled data after learning the linear classifier in SBDAE was assessed. As shown in Table 2, doing so further improves the performance over using labeled data only. This justifies that it is possible to bootstrap from a relatively small amount of labeled data and learn better representations with more unlabeled data with SBDAE.

To gain more insights of the results, the filters learned by SBDAE and DAE are further visualized on the IMDB dataset in Table 3. In particular, the top 5 most activated and deactivated words of the first 8 filters (corresponding to the first 8 rows of W) of SBDAE and DAE, respectively, are shown. First of all, it seems very difficult to make sense of the filters of DAE as they are mostly common words with no clear co-occurrence pattern. By comparison, the filters from SBDAE are mostly sensitive to words that demonstrate clear polarity. In particular, all the 8 filters seem to be most activated by certain negative words, and are most deactivated by certain positive words. In this way, the activation of each filter of SBDAE is much more indicative of the polarity than that of DAE, which explains the better performance of SBDAE over DAE. Note that this difference only comes from reweighting the reconstruction errors in a certain way, with no explicit usage of labels.

The present technology falls into the general category of learning representations for text data. In particular, there have been a lot of efforts that try to learn compact representations for either words or documents [Turney and Pantel 2010; Blei, Ng, and Jordan 2003; Deerwester et al. 1990; Mikolov et al. 2013; Le and Mikolov 2014; Maas et al. 2011]. LDA [Blei, Ng, and Jordan 2003] explicitly learns a set of topics, each of which is defined as a distribution on words; a document is thus represented as the posterior distribution on topics, which is a fixed-length, non-negative vector. Closely related are matrix factorization models such as LSA [Deerwester et al. 1990] and Non-negative Matrix Factorization (NMF) [Xu, Liu, and Gong 2003]. While LSA factorizes the docterm matrix via Singular Value Decomposition, NMF learns non-negative basis and coefficient vectors. Similar to these efforts, the present technology also works directly on the doc-term matrix. However, thanks to the usage of autoencoder, the representation for documents are calculated instantly via direct matrix product, which eliminates the need of expensive inference. The present technology distinguishes itself as a semisupervised representation learning model, where label information can be effectively leveraged.

Recently, there has also been an active thread of research on learning word representations. Notably, [Mikolov et al. 2013] shows learning of interesting word embeddings via very simple architecture on a large amount of unlabeled dataset. Moreover, [Le and Mikolov 2014] proposed to jointly learn representations for sentences and paragraphs together with words in a similar unsupervised fashion. The present technology does not require explicit modelling of the representations for words, but it is straightforward to incorporate such modelling by adding an additional linear layer at the bottom of the autoencoder. Further, various other aspects of semantic data analysis and processing, as well as use in databases, social networks, newsfeeds, environmental monitoring (e.g., security cameras, telephones, call-centers, smartphone apps, etc.), may be implemented, improved, facilitated, or integrated, using the technology. The various references cited herein, each of which is expressly incorporated herein by reference it their entirety, detail various applications, preprocessing, postprocessing, and techniques that may be used in conjunction with the disclosed features. For example, in a human machine interface context, the sentiment analysis may be used to adapt the user interface, to the sentiments expressed, thus improving the human machine interface per se.

From the perspective of machine learning methodology, the present approach resembles the idea of layer-wise pretraining in deep Neural Networks [Bengio 2009]. The model differs from the traditional training procedure of autoencoders in that the label information is effectively utilized to guide the representation learning. A related idea was proposed in [Socher et al. 2011], where they train Recursive autoencoders on sentences jointly with prediction of sentiment. Due to the delicate recursive architecture, their model only works on sentences with given parsing trees, and could not generalize to documents. MTC [Rifai et al. 2011a] is another work that models the interaction of autoencoders and classifiers. However, their training of autoencoders is purely unsupervised, the interaction comes into play by requiring the classifier to be invariant along the tangents of the learned data manifold. It is not difficult to see that the assumption of MTC would not hold when the class labels did not align well with the data manifold, which is a situation the present model does not suffer from.

An extension to prior autoencoders is provided, for learning task-specific representations for textual data. The traditional autoencoders are generalized, by relaxing their loss function to the Bregman Divergence, and then a discriminative loss function derived from the label information.

Experiments on text classification benchmarks have shown that the technology significantly outperforms “Bag of Words”, a traditional Denoising Autoencoder, and other competing methods. The model successfully learns discriminative features, which unsupervised methods typically fail to do.

It is noted that the application of sentiment analysis is but one application of the underlying technology. In fact, various dimensions may be analyzed using the autoencoder, such as feminine-masculine, anger, fear, courage, sadness, tender, joy, disgust, trust, acceptance, anticipation, expectation, surprise, friendship/enmity, shame, confidence, kindness, pity, indignation, envy, love, etc. (See, simple.wikipedia.org/wiki/List_of_emotions: Simple emotions: discovery-anger; envy-no surprise-expectation; wonder-surprise-commonplace; happiness-sadness; amusement-weariness; courage-timidity-cowardice; and pity-cruelty; Complex emotions: pride-modesty-shame; closeness-detachment-distance; complaint/pain-doing average-pleasure; caution-boldness-rashness; patience-mere tolerance-anger; relaxation-composure-stress; and envy-goodwill; Pure emotions: fear-nervousness-security; togetherness-privacy; respect-disrespect; appreciation-envy; love-no love lost-hatred; hope-despair; and confusion-being confused.)(See en.wikipedia.org/wiki/Emotion: Affection, Anger, Angst, Anguish, Annoyance, Anticipation, Anxiety, Apathy, Arousal, Awe, Boredom, Confidence, Contempt, Contentment, Courage, Curiosity, Depression, Desire, Despair, Disappointment, Disgust, Distrust, Ecstasy, Embarrassment, Empathy, Envy, Euphoria, Fear, Frustration, Gratitude, Grief, Guilt, Happiness, Hatred, Hope, Horror, Hostility, Humiliation, Interest, Jealousy, Joy, Loneliness, Love, Lust, Outrage, Panic, Passion, Pity, Pleasure, Pride, Rage, Regret, Remorse, Resentment, Sadness, Saudade, Schadenfreude, Self-confidence, Shame, Shock, Shyness, Sorrow, Suffering, Surprise, Trust, Wonder, Worry.)

Further, the system can learn the orthogonal concepts, using traditional machine learning technologies. For example, principal component analysis, and the related singular value decomposition, may be used to define and extract linearly uncorrelated (or weakly correlated) variables from a dataset. See, en.wikipedia.org/wiki/Principal_component_analysis; en.wikipedia.org/wiki/Singular_value_decomposition.

Rather than implementing an autoencoder that makes a binary determination along an orthogonal axis, the technology may also be used to classify data as belonging to different clusters. See, en.wikipedia.org/wiki/Cluster_analysis. That is, a decision may be made whether a document should be classified within either of two clusters within a data space. The technology may also be extended to higher dimensions, and therefore is not limited to a simple binary determination. When considering higher dimensions, one option is to classify the data pairwise along each possible axis. The result may be a simple binary classification, or a classification, along with some metadata, such as the strength of the association, and the statistical uncertainty. Another option is to extend the autoencoder itself to higher dimensionality. See, en.wikipedia.org/wiki/Autoencoder; en.wikipedia.org/wiki/Dimensionality_reduction.

Textual information may be received. The textual information may include any language information such as text documents, text corpora, data bases, images, social media, e-mails, subtitles, recognized speech, etc. The textual information may be received from another system or retrieved from storage or another system. The textual information may include multiple documents of the same or different type and/format. A universal representation corresponding to the textual information may be obtained. The universal representation may be generated based on the textual information. In some embodiments, the textual information may be subjected to specific processing based on exhaustive technologies using a large number of natural language and universal semantic descriptions. The information may be processed using analysis including lexical-morphological, syntactic, semantic and ontological stages of analysis with identification of the lexical and semantic meanings/values for each element of information, construction of the corresponding data structures at each stage, and extraction of the corresponding features and attributes at each stage. These data structures may be indexed and stored in memory.

As a result, any text information may be transformed into a universal representation and stored in a unified language-independent form, which is subjected to indexing with all the capabilities derived therefrom. The concepts and their attributes may be indexed, since any concept (i.e., an assertion expressed in universal terms) may be enumerated, recorded, and found (searchable). This universal representation of text information may be a unified platform for constructing practically any NLP application. In some embodiments, the universal representation may include semantic class information for each word in the textual information.

Thus, knowledge accumulated the system about the language(s) and the world (semantics) may utilized. The disclosed system provides integrity, comprehensiveness and universality. For example, it may be sufficient to construct linguistic descriptions of a new language according to the standards of the present approach (represented by this disclosure and a group of parent applications incorporated herein by reference), and not only one or more applications, but entire series of said applications become accessible.

Preliminary processing of a text corpus may include at least the following steps: identifying morphological values, identifying lexical meanings, identifying semantic meanings, identifying ontological objects, and indexing the values, parameters and attributes extracted. This may allow for use of a semantic index, rather than an ordinary one, in applications.

Exemplary hardware includes at least one processor coupled to a memory. The memory may include random access memory (RAM) devices, cache memories, non-volatile or back-up memories such as programmable or flash memories, read-only memories (ROM), etc. In addition, the memory may be considered to include memory storage physically located elsewhere in the hardware, e.g. any cache memory in the processor as well as any storage capacity used as a virtual memory, e.g., as stored on a mass storage device.

The hardware may receive a number of inputs and outputs for communicating information externally. For interface with a user or operator, the hardware may include one or more user input devices (e.g., a keyboard, a mouse, imaging device, scanner, microphone) and a one or more output devices (e.g., a Liquid Crystal Display (LCD) panel, a sound playback device (speaker)). To embody the present invention, the hardware may include at least one screen device.

For additional storage, as well as data input and output, and user and machine interfaces, the hardware may also include one or more mass storage devices, e.g., a floppy or other removable disk drive, a hard disk drive, a Direct Access Storage Device (DASD), an optical drive (e.g. a Compact Disk (CD) drive, a Digital Versatile Disk (DVD) drive) and/or a tape drive, among others. Furthermore, the hardware may include an interface with one or more networks (e.g., a local area network (LAN), a wide area network (WAN), a wireless network, and/or the Internet among others) to permit the communication of information with other computers coupled to the networks. It should be appreciated that the hardware typically includes suitable analog and/or digital interfaces between the processor and each of the components is known in the art.

The hardware operates under the control of an operating system, and executes various computer software applications, components, programs, objects, modules, etc. to implement the techniques described above. Moreover, various applications, components, programs, objects, etc., collectively indicated by application software, may also execute on one or more processors in another computer coupled to the hardware via a network, e.g. in a distributed computing environment, whereby the processing required to implement the functions of a computer program may be allocated to multiple computers over a network.

In general, the routines executed to implement the embodiments of the present disclosure may be implemented as part of an operating system or a specific application, component, program, object, module or sequence of instructions referred to as a “computer program.” A computer program typically comprises one or more instruction sets at various times in various memory and storage devices in a computer, and that, when read and executed by one or more processors in a computer, cause the computer to perform operations necessary to execute elements involving the various aspects of the invention. Moreover, while the technology has been described in the context of fully functioning computers and computer systems, those skilled in the art will appreciate that the various embodiments of the invention are capable of being distributed as a program product in a variety of forms, and may be applied equally to actually effect the distribution regardless of the particular type of computer-readable media used. Examples of computer-readable media include but are not limited to recordable type media such as volatile and non-volatile memory devices, removable disks, hard disk drives, optical disks (e.g., Compact Disk Read-Only Memory (CD-ROMs), Digital Versatile Disks (DVDs)), flash memory, etc., among others. Another type of distribution may be implemented as Internet downloads. The technology may be provided as ROM, persistently stored firmware, or hard-coded instructions.

While certain exemplary embodiments have been described and shown in the accompanying drawings, it is understood that such embodiments are merely illustrative and not restrictive of the broad invention and that the present disclosure is not limited to the specific constructions and arrangements shown and described, since various other modifications may occur to those ordinarily skilled in the art upon studying this disclosure. The disclosed embodiments may be readily modified or re-arranged in one or more of its details without departing from the principals of the present disclosure.

Implementations of the subject matter and the operations described herein can be implemented in digital electronic circuitry, computer software, firmware or hardware, including the structures disclosed in this specification and their structural equivalents or in combinations of one or more of them. Implementations of the subject matter described in this specification can be implemented as one or more computer programs, i.e., one or more modules of computer program instructions, encoded on one or more computer storage medium for execution by, or to control the operation of data processing apparatus. Alternatively, or in addition, the program instructions can be encoded on an artificially-generated propagated signal, e.g., a machine-generated electrical, optical, or electromagnetic signal, that is generated to encode information for transmission to suitable receiver apparatus for execution by a data processing apparatus. A computer storage medium can be, or be included in, a computer-readable storage device, a computer-readable storage substrate, a random or serial access memory array or device, or a combination of one or more of them. Moreover, while a non-transitory computer storage medium is not a propagated signal, a computer storage medium can be a source or destination of computer program instructions encoded in an artificially-generated propagated signal. The computer storage medium can also be, or be included in, one or more separate components or media (e.g., multiple CDs, disks, or other storage devices).

Accordingly, the computer storage medium may be tangible and non-transitory. All embodiments within the scope of the claims should be interpreted as being tangible and non-abstract in nature, and therefore this application expressly disclaims any interpretation that might encompass abstract subject matter.

The present technology provides analysis that improves the functioning of the machine in which it is installed, and provides distinct results from machines that employ different algorithms.

The operations described in this specification can be implemented as operations performed by a data processing apparatus on data stored on one or more computer-readable storage devices or received from other sources.

The term “client or “server” includes a variety of apparatuses, devices, and machines for processing data, including by way of example a programmable processor, a computer, a system on a chip, or multiple ones, or combinations, of the foregoing. The apparatus can include special purpose logic circuitry, e.g., an FPGA (field programmable gate array) or an ASIC (application-specific integrated circuit). The apparatus can also include, in addition to hardware, a code that creates an execution environment for the computer program in question, e.g., a code that constitutes processor firmware, a protocol stack, a database management system, an operating system, a cross-platform runtime environment, a virtual machine, or a combination of one or more of them. The apparatus and execution environment can realize various different computing model infrastructures, such as web services, distributed computing and grid computing infrastructures.

A computer program (also known as a program, software, software application, script, or code) can be written in any form of programming language, including compiled or interpreted languages, declarative or procedural languages, and it can be deployed in any form, including as a stand-alone program or as a module, component, subroutine, object, or other unit suitable for use in a computing environment. A computer program may, but need not, correspond to a file in a file system. A program can be stored in a portion of a file that holds other programs or data (e.g., one or more scripts stored in a markup language document), in a single file dedicated to the program in question, or in multiple coordinated files (e.g., files that store one or more modules, sub-programs, or portions of code). A computer program can be deployed to be executed on one computer or on multiple computers that are located at one site or distributed across multiple sites and interconnected by a communication network.

The processes and logic flows described in this specification can be performed by one or more programmable processors executing one or more computer programs to perform actions by operating on input data and generating output. The architecture may be CISC, RISC, SISD, SIMD, MIMD, loosely-coupled parallel processing, etc. The processes and logic flows can also be performed by, and apparatus can also be implemented as, special purpose logic circuitry, e.g., an FPGA (field programmable gate array) or an ASIC (application specific integrated circuit).

Processors suitable for the execution of a computer program include, by way of example, both general and special purpose microprocessors, and any one or more processors of any kind of digital computer. Generally, a processor will receive instructions and data from a read-only memory or a random access memory or both. The essential elements of a computer are a processor for performing actions in accordance with instructions and one or more memory devices for storing instructions and data. Generally, a computer will also include, or be operatively coupled to receive data from or transfer data to, or both, one or more mass storage devices for storing data, e.g., magnetic, magneto-optical disks, or optical disks. However, a computer need not have such devices. Moreover, a computer can be embedded in another device, e.g., a mobile telephone (e.g., a smartphone), a personal digital assistant (PDA), a mobile audio or video player, a game console, or a portable storage device (e.g., a universal serial bus (USB) flash drive). Devices suitable for storing computer program instructions and data include all forms of non-volatile memory, media and memory devices, including by way of example semiconductor memory devices, e.g., EPROM, EEPROM, and flash memory devices; magnetic disks, e.g., internal hard disks or removable disks; magneto-optical disks; and CD-ROM and DVD-ROM disks. The processor and the memory can be supplemented by, or incorporated in, special purpose logic circuitry.

To provide for interaction with a user, implementations of the subject matter described in this specification can be implemented on a computer having a display device, e.g., a LCD (liquid crystal display), OLED (organic light emitting diode), TFT (thin-film transistor), plasma, other flexible configuration, or any other monitor for displaying information to the user and a keyboard, a pointing device, e.g., a mouse, trackball, etc., or a touch screen, touch pad, etc., by which the user can provide input to the computer. Other kinds of devices can be used to provide for interaction with a user as well. For example, feedback provided to the user can be any form of sensory feedback, e.g., visual feedback, auditory feedback, or tactile feedback and input from the user can be received in any form, including acoustic, speech, or tactile input. In addition, a computer can interact with a user by sending documents to and receiving documents from a device that is used by the user. For example, by sending webpages to a web browser on a user's client device in response to requests received from the web browser.

Implementations of the subject matter described in this specification can be implemented in a computing system that includes a back-end component, e.g., as a data server, or that includes a middleware component, e.g., an application server, or that includes a front-end component, e.g., a client computer having a graphical user interface or a Web browser through which a user can interact with an implementation of the subject matter described in this specification, or any combination of one or more such back-end, middleware, or front-end components. The components of the system can be interconnected by any form or medium of digital data communication, e.g., a communication network. Examples of communication networks include a local area network (“LAN”) and a wide area network (“WAN”), an inter-network (e.g., the Internet), and peer-to-peer networks (e.g., ad hoc peer-to-peer networks).

While this specification contains many specific implementation details, these should not be construed as limitations on the scope of any inventions or of what may be claimed, but rather as descriptions of features specific to particular implementations of particular inventions. Certain features that are described in this specification in the context of separate implementations can also be implemented in combination in a single implementation. Conversely, various features that are described in the context of a single implementation can also be implemented in multiple implementations separately or in any suitable subcombination. Moreover, although features may be described above as acting in certain combinations and even initially claimed as such, one or more features from a claimed combination can in some cases be excised from the combination, and the claimed combination may be directed to a subcombination or variation of a subcombination.

Similarly, while operations are considered in a particular order, this should not be understood as requiring that such operations be performed in the particular order shown, in sequential order or that all operations be performed to achieve desirable results. In certain circumstances, multitasking and parallel processing may be advantageous. Moreover, the separation of various system components in the implementations described above should not be understood as requiring such separation in all implementations and it should be understood that the described program components and systems can generally be integrated together in a single software product or packaged into multiple software products.

Thus, particular implementations of the subject matter have been described. Other implementations are within the scope of the following claims. In some cases, the actions recited in the claims can be performed in a different order and still achieve desirable results. In addition, the processes depicted in the accompanying figures do not necessarily require the particular order shown, or sequential order, to achieve desirable results. In certain implementations, multitasking or parallel processing may be utilized.

TABLE 2 Left: our model achieves the best results on four (large ones) out of six datasets. Right: our model is able to take advantage of unlabeled data and gain better performance. books DVD music electronics kitchenware IMDB IMDB + unlabeled BoW 10.76 11.82 11.80 10.41 9.34 11.48 N/A DAE 15.10 15.64 15.44 14.74 12.48 14.60 13.28 DAE+ 11.40 12.09 11.80 11.53 9.23 11.48 11.47 NN 11.05 11.89 11.42 11.15 9.16 11.60 N/A LrDrop 9.53 10.95 10.90 9.81 8.69 10.88 10.73 SBDAE 9.16 10.90 10.59 10.02 8.87 10.52 10.42 SBDAE+ 9.12 10.90 10.58 10.01 8.83 10.50 10.41

TABLE 3 Visualization of learned feature maps. From top to bottom: most activated and deactivated words for SBDAE; most activated and deactivated words for DAE. nothing disappointing badly save even dull excuse ridiculously cannon worst disappointing redeeming attempt fails had dean outrageously unfortunately annoying awful unfunny stupid failed none lends terrible worst sucks couldn't worst rest ruined teacher predictable poorly convince worst avoid he attempt first tears loved amazing excellent perfect years with classic wonderfully finest incredible surprisingly ? terrific best man helps noir funniest beauty powerful peter recommended hard awesome magnificent unforgettable unexpected excellent cool perfect still terrific scared captures appreciated favorite allows heart long wasn't probably to making laugh TV Someone worst guy fan the give find might yet kids music kind and performances where found goes anyone work years this least before kids away trying now place shows comes ever having poor done least go kind recommend although ending worth find book trying takes instead everyone once interesting before day looks special wife anything wasn't isn't work actors everyone now shows comes American rather watching classic performances someone night away sense around

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What is claimed is:
 1. A method of modelling data, comprising: training an objective function of a linear classifier, based on a set of labeled data, to derive a set of classifier weights; defining a posterior probability distribution on the set of classifier weights of the linear classifier; approximating a marginalized loss function for an autoencoder as a Bregman divergence, based on the posterior probability distribution on the set of classifier weights learned from the linear classifier; and automatically classifying unlabeled data using a compact classifier according to the marginalized loss function.
 2. The method according to claim 1, wherein the marginalized loss function is: D({tilde over (x)},x)=E _(θ˜p(θ))(θ^(T)({tilde over (x)}−x))²=∫(θ^(T)({tilde over (x)}−x))² p(θ)dθ wherein E_(θ˜p(θ)) is an expectation, θ are the classifier weights, and x are the data points.
 3. The method according to claim 1, wherein the autoencoder comprises a neural network, wherein said training comprises training the neural network.
 4. The method according to claim 1, wherein the autoencoder comprises a denoising autoencoder.
 5. The method according to claim 4, wherein the denoising autoencoder is denoised stochastically, and comprises a neural network employing stochastic gradient descent training using randomly selected data samples, wherein a gradient is calculated using back propagation of errors.
 6. The method according to claim 1, wherein said training comprises training the objective function of the linear classifier with a bag of words, wherein the linear classifier comprises a support vector machine classifier with squared hinge loss and l₂ regularization.
 7. The method according to claim 1, wherein said training comprises training the objective function of the linear classifier with a bag of words, wherein the linear classifier comprises a Logistic Regression classifier.
 8. The method according to claim 1, wherein the Bregman divergence is determined assuming that all data samples induce a loss.
 9. The method according to claim 1, wherein the posterior probability distribution on the set of classifier weights is estimated using with a Laplace approximation, wherein the Laplace approximation stochastically estimates the set of classifier weights using a covariance matrix constrained to be diagonal.
 10. The method according to claim 1, wherein the posterior probability distribution on the set of classifier weights is estimated using with a Markov chain Monte Carlo method.
 11. A system for modelling data, comprising: an input port, configured to receive a set of labelled data; a linear classifier; an autoencoder; a compact classifier; and an output port, configured to communicate a classification of at least one unlabeled datum, wherein: an objective function of a linear classifier is automatically trained, based on the set of labeled data, to derive a set of classifier weights; a marginalized loss function for the autoencoder is approximated as a Bregman divergence, based on a posterior probability distribution on the set of classifier weights learned from the linear classifier; and the at least one unlabeled datum is classified using the compact classifier according to the marginalized loss function.
 12. The system according to claim 11, wherein the marginalized loss function is: D({tilde over (x)},x)=E _(θ˜p(θ))(θ^(T)({tilde over (x)}−x))²=∫(θ^(T)({tilde over (x)}−x))² p(θ)dθ wherein E_(θ˜p(θ)) is an expectation, θ are the classifier weights, and x are the data points.
 13. The system according to claim 11, wherein the autoencoder comprises a neural network.
 14. The system according to claim 11, wherein the autoencoder comprises a denoising autoencoder.
 15. The system according to claim 14, wherein the denoising autoencoder is denoised stochastically, and comprises a neural network trained according to stochastic gradient descent training using randomly selected data samples, wherein a gradient is calculated using back propagation of errors.
 16. The system according to claim 11, wherein the objective function of the linear classifier is trained with a bag of words, wherein the linear classifier comprises a support vector machine classifier with squared hinge loss and l₂ regularization.
 17. The system according to claim 11, wherein the objective function of the linear classifier is trained with a bag of words, wherein the linear classifier comprises a Logistic Regression classifier.
 18. The system according to claim 11, wherein the Bregman divergence is determined assuming that all data samples induce a loss.
 19. The system according to claim 11, wherein the posterior probability distribution on the set of classifier weights is automatically estimated using a technique selected from the group consisting of a Laplace approximation, wherein the Laplace approximation stochastically estimates the set of classifier weights using a covariance matrix constrained to be diagonal, and a Markov chain Monte Carlo method.
 20. A non-transitory computer readable medium containing instructions for controlling at least one programmable automated processor to model data, comprising: instructions for training an objective function of a linear classifier, based on a set of labeled data, to derive a set of classifier weights; instructions for defining a posterior probability distribution on the set of classifier weights of the linear classifier; instructions for approximating a marginalized loss function for an autoencoder as a Bregman divergence D_(f)({tilde over (x)},x)=ƒ({tilde over (x)})−ƒ(x)+∇ƒ(x)^(T)({tilde over (x)}−x)), wherein {tilde over (x)},x∈R^(d) are two datapoints, ƒ(x) is a convex function defined on R^(d), based on the posterior probability distribution on the set of classifier weights learned from the linear classifier, wherein θ∈R^(d) are the weights of the linear classifier, and D({tilde over (x)},x)=E_(θ˜p(θ))(θ^(T)({tilde over (x)}−x))²=∫(θ^(T)({tilde over (x)}−x))² p(θ)dθ is the marginalized loss function given p(θ) as an expectation over θ, which is approximated using: $\begin{matrix} {{D\left( {\overset{\sim}{x},x} \right)} = {E_{\theta\sim{\overset{\sim}{p}{(\theta)}}}\left( {\theta^{T}\left( {\overset{\sim}{x} - x} \right)} \right)}^{2}} \\ {= {\left( {\overset{\sim}{x} - x} \right)^{T}{E_{\theta\sim{\overset{\sim}{p}{(\theta)}}}\left( {\theta\theta}^{T} \right)}\left( {\overset{\sim}{x} - x} \right)}} \\ {= {\left( {\overset{\sim}{x} - x} \right)^{T}\left( {{\theta\theta}^{T} + \sum} \right)\left( {\overset{\sim}{x} - x} \right)}} \\ {= {\left( {{\hat{\theta}}^{T}\left( {\overset{\sim}{x} - x} \right)} \right)^{2} + {\left( {\sum\limits^{1/2}\left( {\overset{\sim}{x} - x} \right)} \right)^{T}\left( {\sum\limits^{1/2}\left( {\overset{\sim}{x} - x} \right)} \right)}}} \end{matrix};$ and classifying unlabeled data using a compact classifier according to the marginalized loss function. 